In the past transducers were fabricated and referred to as integral silicon diaphragm pressure transducers. Such devices are fabricated from solid state techniques and basically involve the diffusion or disposition of a force sensitive arrangement of piezoresistors on a silicon diaphragm. The integral silicon diaphragms can be made containing a four active arm Wheatstone Bridge, which integral assembly provides an output proportional to pressure and/or deflection. The stress sensors or piezoresistors are arranged so that under load two elements are put in tension and two in compression.
The term integral is used to denote the fact that the sensors, instead of being secured to the diaphragm by means of an epoxy or glue are actually deposited, diffused or otherwise formed on the silicon diaphragm and are electrically isolated therefrom by means of P-N junctions or epitaxial layers. In any event, the silicon diaphragm is carefully selected so that it exhibits the necessary electrical characteristics so that use can be made of the same to permit the fabrication of accurate and controllable piezoresistive sensing elements.
The diaphragms of the prior art were supplied in varying thicknesses as the thickness determines the rated load and output.
The resultant structure was clamped about its peripheral edge to a suitable housing and responded to forces directed thereat to cause diaphragm deflection and resistivity changes in the sensors according to the deflection.
For a clamped edge diaphragm, the center stress is given by: ##EQU1## WHERE W = P.pi. a.sup.2, and P is the pressure, a is the effective radius of the diaphragm, that radius determined is of the active area as distinguished form the clamped area.
T = DIAPHRAGM THICKNESS
M = reciprocal of Poisson's ratio. The strain is defined as
E = /Y
Y = Young's modules for silicon = 30.times.10.sup.6 p.s.i.
= CENTER STRESS OR STRESS
The natural frequency of a diaphragm is important as it is the frequency at which the diaphragm is most sensitive at or will resonate at. The natural frequency of a clamped diaphragm is given by ##EQU2## and for silicon ##EQU3##
The greater the thickness the higher the natural frequency, while the greater the area the lower the natural frequency is as the natural frequency is inversely proportional to the square of the radius of a diaphragm.
Since silicon has a very high stiffness to density ratio, with a modulus essentially equal to that of steel and a density comparable to aluminum, together with the fact that high piezoresistive coefficients of silicon piezoresistors and small size have resulted in gages with high natural resonant frequencies.
In any event, there is a plurality of transducers which are employed to monitor low frequency operation, such as barometric pressure or ultra-low frequency operations.
Due to the nature of such measurements, there is a desire that such transducers be as low in cost as possible while maintaining highly accurate pressure measurements.
It is therefore an object of the present invention to provide a low cost transducer structure useful for measuring relatively low frequency phenomenon while maintaining highly accurate outputs.